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Question Number 29976 by abdo imad last updated on 14/Feb/18
prove that  ln(Γ(x))= −lnx −γx  +Σ_(n=1) ^∞   (  (x/n)  −ln( 1+(x/n))) with x>0
$${prove}\:{that} \\ $$$${ln}\left(\Gamma\left({x}\right)\right)=\:−{lnx}\:−\gamma{x}\:\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\:\:\frac{{x}}{{n}}\:\:−{ln}\left(\:\mathrm{1}+\frac{{x}}{{n}}\right)\right)\:{with}\:{x}>\mathrm{0} \\ $$

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